Moduli of Generalized Spin Curves, Class Size and Calculus Learning

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Jarvis 9501617 This is an award made under the CAREER program to Professor Tyler Jarvis. This product has both an educational component and a research component. The research will be to study the moduli space of higher spin curves and of different compactifications of the resulting moduli space. In particular he hopes to study the moduli of line and vector bundles on degenerating curves. In education he has two projects. The first is a rigorous study of the effect of class size on students in introductory calculus and the second is to develop a new abstract algebra course for junior level students. The mathematical research in this project falls into the general area of arithmetic geometry -a subject that blends two of the oldest areas of mathematics: number theory and geometry. This combination has proved extraordinarily fruitful - having recently solved problems that withstood generations. Among its many consequences are new error correcting codes. Such codes are essential for both modern computers (hard disks) and compact disks. The educational component falls into the broad area of science curriculum reform which is vital if the nation is to meet its need for scientifically trained adults.